Robophysical Studies of Undulatory Locomotion in Disordered Terrains 

We investigate in a laboratory model how environmental disorder influences undulatory locomotor performance. We constructed a 10-joint limbless robophysical model (0.4m long) with individually actuated servos to control travelling body wave amplitude, wavelength, and phase. The experimental terrain consisted of a 2D obstacle field composed of spherical 3D printed spherical cap–shaped obstacles ("boulders") arranged in a triangular lattice. The robot executed a "serpenoid" gait (motor angle varying sinusoidally in time with constant phase offset between motors) with a wavelength (λ) approximately twice the boulder spacing (d) on the uniform lattice. Terrain disorder was introduced by randomly perturbing boulder positions with displacements drawn from a 2D normal distribution of standard deviation 0<σ/d<1. For each σ/d, we conducted 10 trials, initializing the robot with a random starting position and gait phase while keeping other gait parameters fixed. The robot's motion was recorded using a motion capture system, and displacement was quantified from the tracked positions of the robot's center of geometry. The robot's transport performance decreased from 0.87 ± 0.02 to 0.20 ± 0.10 λ per cycle as σ/d increased from 0 to 1. Performance remained high and nearly constant at small disorder, dropped sharply around σ/d ≈ 0.2, and then plateaued at low values for large disorder (σ/d > 0.4). A numerical multibody simulation quantitatively reproduced the experimental measurements.